# Homework Help: Calculating how fast distance changes between ships

1. Oct 30, 2012

### hsd

1. The problem statement, all variables and given/known data

At noon, ship A is 50km west of ship B. Ship A is sailing south at 30km/h and ship B is sailing north at 20km/h. How fast is the distance between the ships changing at 4:00pm in km/h.

2. Relevant equations

3. The attempt at a solution

http://img822.imageshack.us/img822/2420/shipq2.png [Broken]

but the final answer is coming out wrong

Last edited by a moderator: May 6, 2017
2. Oct 31, 2012

### haruspex

I don't understand the very first line of your answer. Why are you taking the squares of the velocities? Where is the 50km in this? If you substitute t = 0 in your equation, what number should you get?

3. Oct 31, 2012

### AJ Bentley

Ship A is heading south at 30 for 4 hours so travels 120 km. Similarly B travels 80 due north.
So they become separated by 200km north/south.
They are separated by 50 km due east west to begin with.

So the distance between the ships is? (pythagoras).
The angle of the same triangle is also the direction cosine of the motion so you can use that to calculate their mutual speed.